MD83 WENT OVER THE TOP OF ANOTHER ACFT THAT WAS JUST XING THEIR RWY DURING TAXI AFTER LNDG ON THE PARALLEL RWY.

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ON JAN/MON/01; I WAS THE CAPT ON FLT X FROM SEA TO STL. DURING TAXI OUT TO RWY 16L; IT BECAME OBVIOUS THAT THE LCL CTL AND GND CTL POS WERE COMBINED. HOLDING SHORT OF RWY 16L WE ADVISED THE CTL TWR THAT WE WERE READY FOR TKOF. ATC CLRED FLT X INTO POS AND HOLD RWY 16L FOR TFC 1 MI FINAL LNDG RWY 16R. AFTER THE ACFT LANDED ON RWY 16R; ATC CLRED FLT X FOR TKOF ON RWY 16L. DURING THE TKOF ROLL; THERE WAS CONVERSATION ON THE TWR FREQ BTWN ATC AND SOME ACFT OR TUGS ON THE GND FREQ AND BTWN ATC AND THE FLT Y THAT HAD LANDED ON RWY 16R. MY FO AND I HEARD ATC ISSUE HOLD SHORT INSTRUCTIONS TO FLT Y; BUT NEITHER OF US CAUGHT THE READBACK OF THE Y FLT AS WE HAD COMMENCED OUR TKOF ROLL AND WERE IN THE PROCESS OF MAKING PROCEDURAL CHKS AND CALLOUTS. JUST AFTER ROTATION AND GEAR UP; FLT Y XMITTED TO ATC THAT AN ACFT HAD JUST TAKEN OFF OVER THE TOP OF THEM. ATC THEN TOLD FLT Y THAT HE HAD ISSUED INSTRUCTIONS FOR THEM TO TURN L AND HOLD SHORT OF RWY 16L. FLT Y REPLIED THAT HE WAS CLRED TO CROSS RWY 16L TO THE RAMP. NEXT; ATC INSTRUCTED US TO CONTACT DEP CTL. MY FO AND I DID NOT SEE FLT Y ON THE RWY DUE TO LOW VISIBILITY AT THE TIME. I BELIEVE IT WAS AROUND 1200 FT RVR. WE PROCEEDED TO STL. CONTRIBUTING FACTORS: 1) COMBINED GND CTL AND LCL TWR POS LEADING TO CTLR FOCUSING ON PROB ON GND CTL AND NOT HEARING FLT Y'S NON COMPLYING READBACK TO HOLD SHORT OF RWY 16L. 2) CREW NOT HEARING CORRECTLY INSTRUCTIONS TO HOLD SHORT OF RWY 16L. 3) LOW VISIBILITY. 4) MY FAILURE TO RECOGNIZE THESE CONTRIBUTING FACTORS AND THE POTENTIAL FOR A DISASTER BY NOT BEING AWARE OF FLT Y'S READBACK. BUT THEN; I WOULD HAVE TO QUESTION IF AN ABORTED TKOF WOULD HAVE STOPPED MY ACFT PRIOR TO FLT Y ACFT XING AT TXWY N.